High pressure piston and piston/diaphragm metering pumps constructed according to the prior art are often unsuited for many high performance liquid chromatography uses because their mean flow rate, V (mean pumped liquid volume per unit of time), is dependent on feed pressure and on the nature and composition of the pumped liquid. This dependence is due to the compressibility of the pumped liquid and to the resilience of the pump elements involved. Further, in piston/diaphragm pumps, wherein movement of the working piston is transmitted via a working liquid to a flexible diaphragm and therefrom to the pumping chamber, the compressibility of the working liquid must be taken into account. At a given feed pressure a certain portion of the piston stroke is used solely for compressing the aspirated liquid up to feed pressure (compression portion). Thus, the feed pumping portion of the stroke is delayed by a phase angle .phi..sub.1 from bottom dead center of the driving crank. At this phase angle .phi..sub.1 the output valve of the pump opens and the feed portion then lasts until driving crank top dead center (phase angle .pi.). On the other hand, the aspiration portion does not start immediately after top dead center but, instead, is delayed by a phase angle .phi..sub.2 (&gt;.pi.). This delay is caused by expansion of the remaining liquid volume in the pumping chamber and the removal of stress from the pump elements (decompression portion).
The fractions of the total piston movement comprising the compression and decompression portions differ one from the other mainly because of the different volumes of liquid present in the pumping chamber at the beginning of each of said portions. When the driving crank is at bottom dead center, i.e., at the beginning of the compression portion, the total volume of liquid present in the pumping chamber is the sum of the piston stroke volume V.sub.d and the residual volume V.sub.o which remains in the pumping chamber after the end of a feed portion. The liquid volume to be compressed to the feed pressure, p, is therefore V.sub.o +V.sub.d. On the other hand, when the driving crank is at top dead center, i.e., at the beginning of the decompression portion, only the residual volume V.sub.o is present in the pumping chamber. Thus, the total liquid volume to be decompressed from feed pressure to aspiration pressure is only V.sub.o. The influence of any resilient mechanical elements and the working liquid, however, should be equal during the compression and decompression portions. Nevertheless, .phi..sub.2 cannot be directly computed from a known .phi..sub.1 because the ratio of the two phase angles is also dependent on the compressibility of the pumped liquid. In the common case of variable liquid mixtures, the compressibility is dependent on the mixing ratio and properties of the liquid components and also on the feed pressure. Thus, compressibility is not a term which is known or can be assumed to be substantially constant.
For high performance liquid chromatography it is essential that a constant flow rate be maintained independent of feed pressure and the kind and composition of the pumped liquid since the accuracy of the analysis is substantially determined by the accuracy of the flow rate.
According to the prior art, various measurement and control apparatus for metering pumps have been proposed for generating constant and reproducible flow rates independent of high counter pressure, feed pressure, and the kind and composition of the pumped liquid. These prior art measurement and control apparatus can be roughly classified into the following six methods:
(1) Measuring the input or output flow of the pump, comparing the measurement with a predetermined nominal value and correcting the pump adjustment via a control loop consisting of measuring arrangement, comparator, adjusting element and pump. Such arrangements are described, e.g., in U.S. Pat. No. 3,917,531 and in German Pat. No. 2,263,768. These arrangements are disadvantageous in that they are expensive and often require calibration of indirect measuring devices.
(2) Keeping the feed pressure constant by means of a pressure control arrangement independent of the magnitude of flow resistances behind the pump. Such an arrangement is described in Varian Associates publication No. 03-913807-00, published in June, 1978. In such a feed arrangement the effect of a variable feed pressure upon the flow rate is fully avoided but the effect of the compressibility of the pumped liquid is still present. Therefore, in analyses which require programmable variation of the solvent composition a certain flow rate variation is encountered because of the varying compressibility of the pumped liquid.
(3) Continuously measuring the feed pressure downstream from the output valve and increasing the piston frequency as feed pressure increases in order to compensate for the increased liquid compression. See U.S. Pat. No. 3,855,129. This method is disadvantageous in that an individual calibration is necessary for each liquid used and in that the compensation is incomplete when liquid mixtures of varying composition are used.
(4) Using dual piston pumps with one pumping chamber delayed .pi. radians behind the other. In such an arrangement, as described in U.S. Pat. No. 4,137,011, each compression portion of the stroke appears as a fast pressure breakdown which is smoothed by a strong acceleration of the drive during each compression portion. Thus, durations of the compression portions and their contributions to the liquid flow are substantially reduced. By means of additional memory and regulating devices the nominal value for the pressure regulation is automatically adjusted when the flow resistances change. With this arrangement the mean feed flow rate V.sub.p, measured at feed pressure, may be kept substantially constant. However, it is often desired in liquid chromatography to keep the mean aspiration flow rate, V.sub.o, measured at intake pressure, constant because of the direct influence of this flow rate on the quantitative analysis result. To a first approximation the relationship EQU V.sub.p =V.sub.o (1- p)
exists between the two flow rates. Therefore, even though V.sub.p is held constant, there is still a variation of V.sub.o because of the feed pressure p and the compressibility of the pumped liquid.
(5) Using two separate pumps to independently control both the mean aspiration flow rate, V.sub.o, and the pumping pressure p. Examples of such arrangements are described in U.S. Pat. No. 4,003,679 and in U.S. Pat. No. 4,489,163. These references describe a series connection of a metering pump operating at nearly zero pressure and a high pressure pump. The high pressure pump is designed to pressurize all of the liquid delivered by the metering pump to the pressure necessary to overcome the flow resistances beyond the pump. Alternatively, a control element is located between the metering pump and the high pressure pump, said control element regulating the high pressure pump in such a manner that the amount of liquid flowing between the two pumps is equalized. Both arrangements fulfill the requirement for a constant mean aspiration flow rate V.sub.o, but are disadvantageous in that two pumps, instead of one, are required.
(6) Measuring the difference between the internal pressure in the pumping chamber and the feed pressure and moving the piston with a constant linear velocity corresponding to the required flow rate when the difference is zero while at all other times the piston is driven at the highest possible speed. See, e.g., U.S. Pat. No. 4,180,375. Thus, a constant flow rate with regard to the actual feed pressure is achieved. However, this method does not allow the generation of a constant flow rate with regard to decompressed liquid.
An additional use of metering pumps is the generation of mixing gradients, i.e., the controlled change of the composition of a solvent mixture with time. In liquid chromatography this is called gradient elution. The requirements for reproducibility and accuracy of the gradient function are as strict as the requirements for the flow rate during gradient elution.
A technically complicated and expensive arrangement for gradient elution which is known in the prior art comprises the use of a separate metering pump with programmable flow rate for each liquid component. A less expensive prior art arrangement is one wherein the liquid components delivered on the aspiration side of the pump are alternated under program control during the aspiration phase of the pump by means of proportioning valves in the aspiration tube. In this arrangement it is necessary to take into account the decompression portion in the control of the proportioning valves. In prior art method (2), described hereinabove, the input valve is synchronized with the pump drive in such a manner that it opens a constant phase angle .phi. after bottom dead center. The beginning of the proportioning valve control cycle is synchronized with the opening time of the input valve (see, e.g., German patent application No. 2,649,593). Since the delay phase angle is not automatically adjustable, this synchronization can be correct only for a specific compressibility of the pumped liquid.
U.S. Pat. No. 4,128,476, mentioned above with reference to prior art method (4), shows a method wherein the times of the pressure breakdown minima are used as an indicator of the duration of the compression portion. Synchronization of the proportioning valves is accomplished by multiplying the angular duration of the compression portion by a constant which represents the decompression/compression time ratio. However, this synchronization can be correct only for an average compresssibility of the pumped liquid; if the real compressibility differs from this average errors may occur in the synchronization.